The propagation of elastic waves in an oblate spheroidal model has been studied based on the ray theory, with axial symmetry starting from the general formulation of Hamilton's principle. Through certain transformations the wave motion in this curvilinear coordinate system may be treated as a flow problem in the rectangular coordinate system. Two parameters, orthogonal to each other, are introduced to describe the geometry of rays in the three-dimensional space. The inverse problem is formulated in terms of boundary values on the outer surface.